System and method for determining intraocular lens power

ABSTRACT

The present invention discloses systems and methods for determine preoperative estimation of postoperative IOL position (or the EAPD) in accordance with one or both of the following mathematical relationships, which are derived from linear regression: 
       EAPD= S   1 +( S   2 ×AND)+( S   3 ×NT)+( S   4 ×AL),   (1 a )
 
       EAPD= W   1 +( W   2 ×AND)+( W   3 ×RND)+( W   4 ×AL),   (1 b )
 
     where S 1 , S 2 , S 3 , and S 4  for equation (1 a ) and W 1 , W 2 , W 3 , and W 4  for equation (1 b ) are statistically derived linear regression constant coefficients.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Application claims the benefit of priority of co-pending U.S.Utility Provisional Patent Application No. 61/935,004, filed Feb. 3,2014, the entire disclosure of which is expressly incorporated byreference herein.

It should be noted that where a definition or use of a term in theincorporated patent application is inconsistent or contrary to thedefinition of that term provided herein, the definition of that termprovided herein applies and the definition of that term in theincorporated patent application does not apply.

BACKGROUND OF THE INVENTION

1. Field of the Invention

One or more embodiments of the present invention relate to intraocularlenses (IOL) and more particularly, to systems and methods fordetermining or selection of intraocular lens (IOL) power.

2. Description of Related Art

It is obvious that a more precise determination of IOL estimated power(IOL_(EP)) is an important aspect in providing the appropriate eyesight(e.g., emmetropia, ametropia, etc.) for a subject for a desired vision.In general, measurements of the eye are typically made preoperativelyand an IOL estimated power (or IOL_(EP)) is selected based oncorrelations between the measured values and different lens powersproviding an estimated refractive outcome.

Most commonly used formulas for IOL power calculations for anappropriate refractory outcome require the preoperative estimation ofpostoperative IOL position, known as Estimated Lens (i.e., IOL) Position(or ELP), which is a function of where the IOL would be positionedinside the eye. It is well known that ELP is the largest contributor oferror in the refractive outcome (or the IOL_(EP)). Another term for theestimated IOL lens position (ELP) is the Estimated Anterior PseudophakicDistance (or EAPD). The term Anterior Pseudophakic Distance (or APD) maybe defined as the postoperative, actual distance from the anteriorsurface of the cornea to the anterior surface of the IOL, with EAPDbeing the estimated, preoperative measurement.

Accordingly, in light of the current state of the art and the drawbacksto current system and methodologies for determining IOL power, the needexists for a system and method that would enable a more precisedetermination of EAPD to thereby facilitate a more precise determinationor selection of IOL_(EP) estimated power for a more precise refractiveoutcome.

BRIEF SUMMARY OF THE INVENTION

A non-limiting, exemplary aspect of an embodiment of the presentinvention provides a method for determine preoperative estimation ofpostoperative IOL position, comprising:

determining an axial length (AL) of an eye;

determining Ante-Nucleus Distance (AND), which is a distance from ananterior surface of cornea along an optical axis of the eye to ananterior surface of a natural lens nucleus;

determining Retro-Nucleus Distance (RND), which is a distance from ananterior surface of the natural lens nucleus to a posterior surface of anatural lens capsule;

with an Estimated Anterior Pseudophakic Distance (EAPD) calculatedaccording:

EAPD=W ₁+(W ₁×AND)+(W ₃×RND)+(W ₄×AL),

Where W₁, W₂, W₃, and W₄ are constant coefficients.

Another non-limiting, exemplary aspect of an embodiment of the presentinvention provides method for determine preoperative estimation ofpostoperative IOL position, comprising:

determining an axial length (AL) of an eye;

determining Ante-Nucleus Distance (AND), which is a distance from ananterior surface of cornea along an optical axis of the eye to ananterior surface of a natural lens nucleus;

determining natural lens Nucleus Thickness (NT), which is a distancemeasured along an optical axis from an anterior surface of a lensnucleus to a posterior surface of the lens nucleus;

with an Estimated Anterior Pseudophakic Distance (EAPD) calculatedaccording:

EAPD=S ₁+(S ₂×AND)+(S ₃×NT)+(S ₄×AL),

Where S₁, S₂, S₃, and S₄ are constant coefficients.

Such stated advantages of the invention are only examples and should notbe construed as limiting the present invention. These and otherfeatures, aspects, and advantages of the invention will be apparent tothose skilled in the art from the following detailed description ofpreferred non-limiting exemplary embodiments, taken together with thedrawings and the claims that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

It is to be understood that the drawings are to be used for the purposesof exemplary illustration only and not as a definition of the limits ofthe invention. Throughout the disclosure, the word “exemplary” may beused to mean “serving as an example, instance, or illustration,” but theabsence of the term “exemplary” does not denote a limiting embodiment.Any embodiment described as “exemplary” is not necessarily to beconstrued as preferred or advantageous over other embodiments. In thedrawings, like reference character(s) present corresponding part(s)throughout.

FIG. 1A is a non-limiting, exemplary schematic illustration of asectional profile of an eye, including different distances that aremeasured in accordance with one or more embodiments of the presentinvention;

FIG. 1B is a non-limiting, exemplary illustration of a representation ofa display of the biometric measurement of eye segments in accordancewith one or more embodiments of the present invention;

FIG. 2 is a non-limiting, exemplary schematic illustration of across-sectional profile of the anterior segment of a pseudophakic eye inaccordance with one or more embodiments of the present invention;

FIG. 3A-1 is a non-limiting, exemplary illustration of scattergramchart, comparing the differences between the post-operative APD and thepre-operative AND values to the NT in accordance with one or moreembodiments of the present invention;

FIG. 3A-2 is a non-limiting, exemplary illustration of scattergramchart, comparing the differences between the post-operative APD and thepre-operative AND values to the RND in accordance with one or moreembodiments of the present invention;

FIG. 3B is a non-limiting, exemplary illustration of scattergram chart,comparing the differences between the EAPD and the APD values versus theAL in accordance with one or more embodiments of the present invention;and

FIG. 3C is a non-limiting, exemplary illustration of scattergram chart,comparing the calculated EAPD to the post-operative measured APD inaccordance with one or more embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of presently preferred embodimentsof the invention and is not intended to represent the only forms inwhich the present invention may be constructed and or utilized.

The present invention provides systems and methods that enable a moreprecise determination of preoperative estimation of postoperative IOLposition (the EAPD) to thereby facilitate a more precise determinationor selection of IOL_(EP) estimated power for a more precise refractiveoutcome.

FIG. 1A is a non-limiting, exemplary schematic illustration of across-sectional profile of different structures of an eye (where thenatural lens is still in place), and different distances that aremeasured in accordance with one or more embodiments of the presentinvention. The overall anatomy of the eye is very well known and hence,various ophthalmic structures of the phakic eye 100 in FIG. 1A will bedescribed in view of the distances measured.

As illustrated in FIG. 1A, general, the natural lens 110 (with anteriorsurface 110 a and posterior surface 110 b) is comprised of a lensnucleus 112 (with anterior surface 112 a and posterior surface 112 b)that is a surrounded by a lens cortex 114 (with anterior surface 114 aand posterior surface 114 b), encapsulated within a lens capsule 116(with anterior surface 116 a and posterior surface 116 b), forming thenatural lens 110. In other words, the lens nucleus 112 of the naturallens 110 is fully surrounded within a cortical material (soft materialthat comprise or form the lens cortex 114), with both the lens nucleus112 and its surrounding lens cortex 114 secured (or encapsulated) withinthe lens capsule 116. In most cases, it is the lens cortex 114 (theanterior surface 114 a of the lens cortex 114) that is mostly affectedin terms of significant variations or changes in its shape due to anynumber of ophthalmic issues such as cataract, which, in turn, affectsthe shape of the lens capsule 116 and somewhat the lens nucleus 112.This, in turn, affects the refractory outcome of the eye.

Anterior cortical deformations in particular, introduce significanterrors to the conventional EAPD measurements and specifically, to EAPDmeasurements that rely on the span of the Anterior Chamber Depth (ACD).The ACD is defined, as a distance measured along an optical axis fromthe anterior surface 104 a of the cornea 104 to the anterior surface 110a of the natural lens 110, which is the anterior surface 116 a of thelens capsule 116 behind (or within) which, may be a deformed lens cortex114 (the anterior portion 114 a). This deformation of the lens cortex114 makes the ACD parameter for calculating a more precise EAPDunreliable.

Further, in most instances (including in those with cataract eye), thelens cortex 114 and the lens nucleus 112 are removed (known asphacoemulsification) from the lens capsule 116, which cause the capsule116 to collapse, making measurements with respect to natural LensThickness (LT) useless, in particular when accounting for the fact thatthe replacement IOL has a different dimension than the LT of the naturallens 110 and further, may be positioned within the lens capsule 116 at adifferent focal position. The present invention defines natural lensthickness LT as the distance measured along an optical axis from theanterior lens capsule surface 116 a to the posterior lens capsulesurface 116 b of the natural lens 110, which includes the lens cortex114 and the lens nucleus 112. Accordingly, both ACD and LT measurementsare at best very rough approximations, introducing significant errors tothe overall calculations for EAPD and hence, eventually IOL power due todeformities of the lens cortex 114.

FIG. 2 is a non-limiting, exemplary schematic illustration of across-sectional profile of the anterior segment of a pseudophakic eye(where the natural lens is replaced by IOL). As illustrated and furtherdescribed below, one or more embodiments of the present inventionincorporate new measurements that provide a superior prediction of anAnterior Pseudophakic Distance (APD) with more precise results (shown inFIG. 2) of IOL_(EP) estimated power. As indicated above and now inrelation to FIG. 2, APD may be defined as the postoperative, actualdistance from the anterior surface 104 a of the cornea 104 to theanterior surface 202 a of the IOL 202. APD may be measured in a varietyof different ways after surgery, non-limiting example of which mayinclude the use of the well-known LENSTAR LS 900® by HAAG-STREITDIAGNOSTICS from Switzerland.

Referring back to FIG. 1A, as indicated above, in order to calculate,determine, or estimate the power of IOL 202 (FIG. 2) that is able toprovide a predetermined refractive outcome, various dimensions ormeasurements of the eye 100 are made prior to the surgical procedure.Various ophthalmic measurements in accordance with the present inventionmay be performed using any number of well known conventional machines(optical or ultrasound). A non-limiting example of an optical biometricmachine that may be used for determining various ophthalmic measurementsmay include the above mentioned LENSTAR LS 900® by HAAG-STREITDIAGNOSTICS from Switzerland. It should be noted that the variousophthalmic measurements in accordance with the present invention may beperformed and obtained using one-dimensional calculations (linearlyalong an optical axis, best shown in FIG. 1B, which were obtained usingLENSTAR LS 900®) or in two-dimensions (planer imagery).

As illustrated in FIGS. 1A to 3C, the present invention provides systemsand methods for determine preoperative estimation of postoperative IOLposition (or the EAPD) in accordance with one or both of the followingmathematical relationships, which are derived from linear regression:

EAPD=S ₁+(S ₂×AND)+(S ₂×NT)+(S ₄×AL),   (1a)

EAPD=W ₁+(W ₂×AND)+(W ₃×RND)+(W ₄×AL),   (1b)

where S₁, S₂, S₃, and S₄ for equation (1a) and W₁, W₂, W₃, and W₄ forequation (1b) are statistically derived linear regression constantcoefficients (detailed below). The calculations of EAPD using equation(1a) are based on measurements of the Axial Length (or AL), Ante-NucleusDistance (or AND that is further detailed below), and natural lensNucleus Thickness (or NT that is further detailed below), andcalculations using equation (1b) are based on measurements of the AL,AND, and Retro-Nucleus Distance (or RND that is further detailed below).

As detailed below, both of the EAPD equations (1a) and (1b) arestatistically equal and as indicated below, may be equally (at leaststatistically equally) used to determine the estimated IOL_(EP) power.However, which EAPD equation ((1a) and or (1b)) to use depends on thetype of optical biometric machine being used and whether the opticalbiometric machine is capable of determining the values of the variablesin equations (1a) or (1b). For example, certain optical biometricmachines can directly calculate the values of NT in which case, equation(1a) may be used and others, may not have the capability to directlymeasure NT in which case, equation (1b) may be used. Accordingly, thetype of EAPD equation (1a) and or (1b) used is dictated by thecapability limits of the optical biometric machine.

Referring to equations (1a) and (1b), AL in equations (1a) and (1b) isdefined as a distance from an anterior surface 104 a of cornea 104 alongan optical axis of the eye 100 to an anterior surface of the retina 118within a fovea region of the eye. The optical axis is a reference linealong which light propagates through the eye. AND in equations (1a) and(1b) is a distance from an anterior surface 104 a of cornea 104 along anoptical axis of the eye 100 to an anterior surface 112 a of a naturallens nucleus 112, thus advantageously bypassing the irregularitiesassociated with the anterior portion 114 a of the natural lens cortex114. The prefix “ante” in AND is referring to the space or span that islocated before the natural lens nucleus 112 or preceding the naturallens nucleus 112. Another advantage of AND measurement is that theoverall EAPD is determined from a closer distance or nearer to theposition where the IOL would replace the natural lens 112, which is theanterior surface 112 a of the nucleus 112 of the natural lens 110,rather than approximations from a farther distance of anterior surface116 a of the lens capsule 116. That is, estimating the preoperativeposition of the IOL nearer to where the postoperative position of IOLwould be positioned is within a more confined space occupied by thenatural lens nucleus 112 (resulting in a more precision approximation)rather than the more expansive space occupied by the entire natural lens110 that may also include a deformed lens cortex 114.

The AND in equations (1a) and (1b) may be determined as follows:

AND=ACD+ACX,   (2)

where ACD in equation (2) is the Anterior Chamber Depth, defined as adistance from an anterior surface 104 a of cornea 104 along an opticalaxis of the eye 100 to an anterior surface 110 a of the natural lens 110(which is the anterior surface 116 a of the lens capsule 116). The ACXin equation (2) is the Anterior Cortical Space defined by a distancefrom the anterior surface 110 a of the natural lens 110 (which is theanterior surface 116 a of the lens capsule 116) along an optical axis ofthe eye 100 to the anterior surface 112 a of the lens nucleus 112. Ingeneral, if the AND value is shallow (closer to the cornea 104 along theoptical axis), the IOL approximate anterior position will most likely bepredicatively positioned closer towards the cornea 104 and if AND valueis longer (has more depth), the IOL approximate anterior position willmost likely be predicatively positioned further from the cornea 104.

The NT in equation (1a) is defined as a distance measured along anoptical axis from an anterior surface 112 a of the lens nucleus 112 to aposterior surface 112 b of the lens nucleus 112. In general, if the NThas a low value (closer to the cornea 104 along the optical axis), theIOL will most likely be predicatively positioned closer towards thecornea 104 and if the NT has a high value, the IOL approximate positionwill most likely be predicatively positioned further from the cornea104.

The RND in equation (1b) is a distance from an anterior surface 112 a ofthe natural lens nucleus 112 to a posterior surface 116 b of a naturallens capsule 116. The prefix “retro” in RND is referring to span that islocated behind nucleus 112 (anterior surface 112 a thereof). In general,if the RND has a low value (closer to the cornea 104 along the opticalaxis), the IOL will most likely be predicatively positioned closertowards the cornea 104 and if the RND has a high value, the IOLapproximate position will most likely be predicatively positionedfurther from the cornea 104.

The RND in equation (1b) may be determined as follows:

RND=(NT+PCX)=(LT−ACX),   (3)

where NT in equation (3) is lens nucleus thickness, which is defined asa distance measured along an optical axis from an anterior surface 112 aof the lens nucleus 112 to a posterior surface 112 b of the lens nucleus112. The PCX in equation (3) is the posterior cortical space defined bya distance from the posterior surface 112 b of the natural lens nucleus112 along an optical axis of the eye 100 to the posterior surface 110 bof the lens 110 (which is the posterior surface 116 b of the lenscapsule 116). The LT is the distance measured along an optical axis fromthe anterior lens capsule surface 116 a to the posterior lens capsulesurface 116 b of the natural lens 110, which includes the lens cortex114 and the lens nucleus 112. The ACX is the anterior cortical spacedefined by a distance from the anterior surface 110 a of the naturallens 110 (which is the anterior surface 116 a of the lens capsule 116)along an optical axis of the eye 100 to the anterior surface 112 a ofthe lens nucleus 112.

It should be noted that since the IOL 202 replaces the natural lensnucleus 112 within the natural lens capsule 116 rather than replacingthe entire natural lens 110, determining the position or location of thelens nucleus 112 where the IOL 202 is supposed to be positioned andreplace is a more precise measurement than the location of the entirenatural lens 110. Therefore, the above AND, NT, and RND measurementsestimate the preoperative position of the IOL nearer to where thepostoperative position of IOL would be positioned, which is the moreconfined space occupied by the natural lens nucleus 112 rather than themore expansive (or larger volume of) space occupied by the entirenatural lens 110 that may also include a deformed lens cortex 114,providing a substantially improved estimated IOL_(EP) power.

FIG. 1B is a representative display of the biometric measurement of thedifferent eye segments using the above-mentioned LENSTAR LS 900®biometer. The following illustrated spikes are noted on the graph,identifying from left to right, the anterior surface of the cornea 104a, the posterior surface of the cornea 104 b, the anterior surface ofthe natural lens 110 a or anterior surface of lens capsule 116 a, theanterior surface of the natural lens nucleus 112 a, the posteriorsurface of the natural lens nucleus 112 b, the posterior surface of thenatural lens 110 b or posterior surface of the lens capsule 116 b, theretinal surface 118 and the pigment epithelium layer 120.

The indicators 122 displayed at the tip of the two conical spikes (104 aand 104 b), the two natural lens or lens capsule spikes (110 a/ 116 aand 116 b), the retinal spike (118) and the pigment epithelium layerspike (120) are used to measure distances between the differentindicators 122 to automatically generate the axial length of the eye(AL), the anterior chamber depth ACD, and the lens thickness (LT).

In addition to the conventionally measured ophthalmic parameters (of AL,ACD, and LT), additional measurements are further obtained in accordancewith one or more embodiments of the present invention. The one or moreembodiments of the present invention further determine measurements forthe ophthalmic parameters ACX, NT, and PCX to further calculate the ANDand the RND, all of which are used in equations (1a) and (1b) above.

The resulting calculated EAPD from equations (1a) or (1b), which isfurther detailed below, may be used in a number of lens power (orrefractive) calculations. The following is one, non-limiting example ofIOL power calculations (for discussion purposes) using the well-knownthin lens methodology applied to a two-lens system (cornea and IOL). Ofcourse, the resulting EAPD from equations (1a) or (1b) may equally beapplied to or used within other well-known IOL power calculationformulas such as those that use ray tracing.

$\begin{matrix}{{IOL}_{EP} = {\frac{n_{AH}}{{AL} - {EAPD}} - \frac{1}{\frac{1}{K + R_{C}} - \frac{EAPD}{n_{AH}}}}} & (4)\end{matrix}$

In equation (4), IOL_(EP) is the estimated power of IOL, n_(AH) is theindex of refraction for the aqueous humor (approximately 1.336), K iscorneal power, AL is axial length of the eye, and R_(C) is refractiveerror at the corneal plane.

The refractive power of cornea is determined by measuring a radius ofcurvature of the cornea (CR), and converting the cornea radius into acorneal refractive power K using index of refraction. Corneal power maybe determined by a number of well known methods. The present inventionused the Scheimpflug principle to more precisely determine the cornealpower, which is an index of refraction of 1.329 rather than the standardindex of refraction of 1.3375 used by others (see for example H. JohnShammas, MD et. al., “Scheimpflug photography keratometry readings forrouting intraocular lens power calculation” J Cataract Refract Surg2009; 35:330-334, which is herein incorporated by reference in itsentirety). The refractive error at the corneal plane R_(C) is theprescription of the glass as if using a contact lens. The advantage ofusing R_(C) is that one can add this error to the overall corneal powerto estimate the overall power of the IOL_(EP). R_(C)=0 is used tocalculate IOL_(EP) for emmetropia, with IOL_(EP) for ametropia iscalculated using the spectacle refraction Rs=Rc/(1+0.012Rc). R_(C), itscalculations, use, and purpose are well known.

NON-LIMING EXAMPLES

The following discussions are related to determining or derivingspecific constants for equations (1a) and (1b), which are based on alimited number of specific case studies. As will be apparent to thoseskilled in the art, the constants in equations (1a) and (1b) will varyfrom the below exemplary calculations and be affected depending on manyfactors, non-limiting, non-exhaustive listing of examples of which mayinclude the model/type of IOL used, the type and the manner in which anophthalmic surgery is performed, the experience of the physicianperforming the surgery, whether the phacoemulsification was uneventfulor had complications, and etc.

As indicated above, the present invention provides systems and methodsfor determining preoperative estimation of postoperative IOL positive(or the EAPD) in accordance with the above equations (1a) or (1b).Measurements for the ophthalmic parameters AL, AND, RND, and NT inequations (1a) or (1b) may be obtained using the well-known LENSTAR LS900® biometer. However, the respective constant coefficients of S₁, S₂,S₃, and S₄ for equation (1a) and W₁, W₂, W₃, and W₄ for equation (1b)are statistically derived. A non-limiting, exemplary statisticalanalysis that may be used for statistical derivation of the values ofthe constant coefficients for equations (1a) and (1b) may include theuse of linear regression in general, with further evaluations using bothsingle regression and sequential regression. In this non-limitingexemplary instance, the present invention applies linear regression todata (charted in FIGS. 3A to 3C) obtained by evaluating patients thatunderwent cataract surgery.

The present invention evaluated ninety eyes of 90 consecutive patientswith no other ocular pathology who had uneventful phacoemulsificationcataract surgery. If both eyes had cataract surgery only the firstoperated eye was included in the study to avoid data duplication. Theinventor of the present invention performed all surgeries. An acrylicIOL (SN60WF, ALCON SURGICAL, INC.™) was placed in the lens capsule 116in all cases. The final refraction was obtained 4 to 5 weeks aftercataract surgery. That is, approximately one month after surgery, theAPD was measured with an optical biometric machine. The post-operativeAPD was then compared to the AL, ACD, LT, K, NT, RND, and AND (allmeasured before the surgery) through regression equations (detailedbelow).

FIG. 3A-1 is a non-limiting, exemplary illustration of scattergramchart, comparing the differences between the post-operative APD and thepre-operative AND values to the NT, with the Y-axis showing measurementsof APD−AND difference values in millimeters, and the X-axis showing themeasurements of the NT in mm. FIG. 3A-2 is a non-limiting, exemplaryillustration of scattergram chart, comparing the differences between thepost-operative APD and the pre-operative AND values to the RND, with theY-axis showing measurements of APD−AND difference values millimeters,and the X-axis showing the measurements of the RND in mm. FIG. 3B is anon-limiting, exemplary illustration of scattergram chart, comparing thedifferences between the EAPD and the APD values versus the AL, with theY-axis showing measurements of EAPD−APD differences values inmillimeters, and the X-axis showing the measurements of the AL in mm.FIG. 3C is a non-limiting, exemplary illustration of scattergram chart,comparing the calculated EAPD to the post-operative measured APD, withthe Y-axis showing measurements of APD values millimeters, and theX-axis showing the calculated EAPD in mm.

The data from the scattergram charts of FIGS. 3A-1 to 3C was evaluatedto derive the Pearson-Moment Correlation Coefficients R, which aretabulated in Table 1 and Table 2 below, resulting in the following EAPDformulas, the derivations of which are further detailed below.

EAPD=AND+0.386 NT−0.749+0.015 (AL−23.50)   (5)

EAPD=AND+0.315 RND−0.677+0.015 (AL−23.50)   (6)

The predicted refractive error is calculated as the difference betweenthe predicted refraction (preoperative) and the actual measuredrefraction (postoperative). A positive value indicates the IOL_(EP)would have left the eye more hyperopic than expected, and a negativevalue indicates that the IOL_(EP) would have left the eye more myopicthan expected.

As tabulated in Tables 1 and 2, regression equations compared thepost-operative anterior pseudophakic distance (APD) to the differentpre-operative measurements. Table 1 shows the correlation coefficient(R) of these different individual relations. Table 1 below establishesthat the highest correlation is between the post-operative APDmeasurement and the pre-operative AND measurement (R=0.81).

As indicated in Table 2, the best fit (R=0.85) was obtained when APD wascorrelated to the AND, NT and AL (equation 1a) or AND, RND and AL(equation 1b). In other words, the equations 1a and 1b are statisticallyequal.

TABLE 1 Correlation co-efficient Value (R) between the post-operativeanterior pseudophakic distance (APD) and the different pre-operativemeasurements to establish main correlating factor Using a singleregression equation R Value APD vs. AL 0.47 APD vs. ACD 0.66 APD vs. LT0.01 APD vs. K 0.20 APD vs. NT 0.16 APD vs. RND 0.11 APD vs. AND 0.81

TABLE 2 Correlation co-efficient Value (R) between the post-operativeanterior pseudophakic distance (APD) and the combination AND and NT, andthe combination AND and RND Using a sequential regression equation RValue APD vs. AND 0.81 APD vs. AND and NT 0.84 APD vs. AND and RND 0.84APD vs. AND, NT, and AL 0.85 APD vs. AND, RND, and AL 0.85

The surgically implanted IOL will be located in the space occupied bythe nucleus. In other words, the post-operative APD value is the sum ofthe AND value and a portion of the lens nuclear thickness (NT). Toevaluate this relationship, the difference between the post-operativeAPD and the pre-operative AND values is compared to the nucleusthickness (NT). As indicated above, FIG. 3A-1 is a non-limiting,exemplary illustration of scattergram chart, comparing the differencesbetween the APD and the pre-operative AND values to the NT, with theY-axis showing measurements of APD−AND difference values in millimeters,and the X-axis showing the measurements of the NT in mm. It is wellknown that the linear regression equation may be represented by:

Y=aX+b,   (7)

where “a” and “b” are constants. In FIG. 3A-1, the line equation of theillustrated trend line 302 may be represented (and in fact calculated)as a linear regression equation:

Y=0.386X−0.749,   (8)

which is determined using the data values of the plotted data. Thepresent invention substitutes the difference (APD−AND), the Y-axis ofthe graph of FIG. 3A-1, for the Y variable in linear regression equation(8), and the NT, which is the X-axis of the graph of FIG. 3A-1, for theX variable in the linear regression equation (8) with the “a” and “b” asthe two constants as follows:

APD−AND=0.386 NT−0.749   (9),

Solving the above equation (9) for APD results in the following equation(10):

APD=AND+0.386 NT−0.749   (10)

Equation (10) can then be used as a way to estimate pre-operatively theAPD value (the EAPD) in equation (1a).

Similarly with respect to equation (1b), the surgically implanted IOL islocated in the space occupied by the nucleus and the posterior cortex,the space that is labeled the retro-nucleus distance (RND). In otherwords, the post-operative APD value is the sum of the AND value and aportion of the retro-nucleus distance (RND). To evaluate thisrelationship, the difference between the post-operative APD and thepre-operative AND values is compared to RND. As indicated above, FIG.3A-2 is a non-limiting, exemplary illustration of scattergram chart,comparing the differences between the post-operative APD and thepre-operative AND values to the RND, with the Y-axis showingmeasurements of APD−AND difference values in millimeters, and the X-axisshowing the measurements of the RND in mm. Using the linear regressionequation (7) in view of the data in FIG. 3A-2, the line equation of theillustrated trend line 304 may be represented (and in fact calculated)as the following linear regression equation:

Y=0.315X−0.677,   (11)

which is determined using the data values of the plotted data. Thepresent invention substitutes the difference (APD−AND), the Y-axis ofthe graph of FIG. 3A-2, for the Y variable in linear regression equation(11), and the RND, which is the X-axis of the graph of FIG. 3A-2, forthe X variable in the linear regression equation (11) with the “a” and“b” as the two constants (of equation (7)) as follows:

APD−AND=0.315 RND−0.677   (12).

Solving the above equation (12) for APD results in the followingequation (13):

APD=AND+0.315 RND−0.677.   (13)

Equation (13) can then be used as a way to estimate pre-operatively theAPD value (the EAPD) in equation (1b).

The inventor also postulates that the axial length AL has a slightinfluence on these equations, especially in the very short and the verylong eyes. To evaluate how the axial length affects the EAPD value, thedifference between EAPD and APD is compared to the axial lengthmeasurement. FIG. 3B is a scattergram comparing the difference betweenthe calculated EAPD and the measured APD value (EAPD−APD) to the axiallength (AL). In FIG. 3B, it is readily apparent that if EAPD is equal tothe APD for all of the values of AL, then all of the ordinate values (orthe Y values) of all of the (X, Y) points defining the trend line 306will be zero (or (X, 0) or (AL, 0)). This means that the value of AL(indicated as the abscissa) is not relevant for cases that EAPD and APDare equal. However, as illustrated, the trend line 306 is not horizontalbut sloped at some angle, with only one single zero crossing (ZC) point(AL_(ZC), 0). Accordingly, in view of the data plotted, thezero-crossing point of the illustrated trend line 306 may be interpretedas the single point (AL_(ZC), 0) where the average of the EAPD valuesand the average of the APD values are equal. This means that at the zerocrossing of the trend line 306 the Y value or the ordinate value of thezero crossing point (AL_(ZC), Y=0) is defined as:

0=EAPD_(AVG)−APD_(AVG),   (14)

In this non-limiting exemplary instance (with ninety patients), thezero-crossing point for the trend line 306 is calculated to be anAL_(ZC) value of 23.5 mm, giving the zero crossing point the full valueof (23.5, 0).

As further indicated by FIG. 3B, portions of the trend line 306 that areabove the zero crossing indicate that the EAPD values are higher thanthe actual APD values, which means that the EAPD has been over-estimatedfir shorter eyes (the distance of which is determined by the AL(represented as the abscissa)). Further, portions of the trend line 306that are below the zero crossing indicate that the EAPD values are lessthan the actual APD values, which means that the EAPD has beenunder-estimated for longer eyes (the distance of which is determined bythe AL).

To correct the estimations (so that EAPD=APD), the over-estimated EAPDvalues (those that are above the zero crossing) must be decreased andthe under-estimated EAPD values (those below the zero-crossing) must beincreased. The compensation value by which the EAPD is increased ordecreased to compensate for over or under estimations of EAPD isdetermined as follows:

$\begin{matrix}\frac{Y_{ZC} + Y}{{{AL}_{ZC} - {AL}}} & (15)\end{matrix}$

Where AL_(ZC) is the AL value of the trend line 306 at its zerocrossing, Y_(ZC) is zero (EAPD=APD) value for the ordinate at zerocrossing of the trend line 306, and AL is another abscissa value on thetrend line 306, Y is another ordinate value on the trend line 306, withthe denominator of equation (15) taking the absolute value of thedifference between two points on the trend line 306 because a negativelength is not possible. In general, since the abscissa representing theAL measurements is given in integers (or whole numbers) in millimeterslength, AL_(ZC) would be 23.5 and Y_(ZC) would be zero (where EAPD=APD).Tracing the trend line 306 starting from zero-crossing at point (23.5,0) and moving a single millimeter along the abscissa above the zerocrossing would identify the trend line point:

$\begin{matrix}{\frac{0 + 0.015}{{23.5 - 22.5}} = \frac{0.015}{1}} & (16)\end{matrix}$

According, the EAPD has been over-estimated by 0.015 (a positive value),requiring an equal compensation reduction to set the EAPD=APD. Tracingthe trend line 306 starting from zero-crossing at point (23.5, 0) andmoving a single millimeter below the zero crossing would identify thetrend line point:

$\begin{matrix}{\frac{0 - 0.015}{{23.5 - 24.5}} = \frac{- 0.015}{1}} & (17)\end{matrix}$

According, the EAPD has been under-estimated by 0.015 (a negativevalue), requiring an equal compensation increase to set the EAPD=APD.Therefore, in this non-limiting exemplary instance, the amount by whichthe over-estimated EAPD must be decreased is found to be approximately0.015 mm and the amount by which the under-estimated EAPD must beincreased is found to be approximately 0.015 min. Accordingly, the firstEAPD equation (1a) that is based on the AND, NT and AL measurementsbecomes:

EAPD=AND+0.386 NT−0.749+0.015 (AL−23.50)   (18a)

It should be noted that the constants 0.386 and −0.749 may vary withdifferent IOL models, manufacturers, surgical procedures, and many otherfactors. The equation (18) includes the compensation values “0.015(AL−23.50)” for over or under estimation, which sets the EAPD=APD forthe non-limiting example of ninety patients.

By solving the arithmetic calculations, Equation 18a can be re-written:

EAPD=−1.1015+AND+0.386 NT+0.015 AL   (18b)

In equation (18b), −1.1015, 1, 0.386 and 0.015 become the S₁, S₂, S₃ andthe S₄ constants that characterize Equation (1a).

The second EAPD equation (1b) that is based on the AND, RND and ALmeasurements becomes:

EAPD=AND+0.315 RND−0.677+0.015 (AL−23.50)   (19a)

As with equation (18a), in the above equation (19a), the constants 0.315and −0.677 may vary with different IOL models, manufacturers, surgicalprocedures, and many other factors. The equation (19) includes thecompensation values “0.015 (AL−23.50)” for over or under estimation,which sets the EAPD=APD for the non-limiting example of ninety patients.

By solving the arithmetic calculations, Equation 19a can be re-written:

EAPD=−1.0295+AND+0.315 RND+0.015 AL   (19b)

In equation (19b), −1.0295, 1, 0.315 and 0.015 become the W₁, W₂, W₃ andthe W₄ constants that characterize Equation (1b).

FIG. 3C is a scattergram comparing the calculated EAPD to thepost-operative measured APD distance (using either of the equations (18)and or (19)). Using the trend line illustrated in FIG. 3C, thecorrelation coefficient (using AL) is determined to be R=0.850(tabulated in Table 2 above), which is an improvement from R=0.840(without using At—tabulated in Table 2 above). In this example, theconstants for both equations (18) and (19) were derived from onespecific IOL make/model from one specific manufacturer. IOL's anteriorradius of curvature, its posterior radius of curvature and its thicknessdetermine the power of an IOL. Different IOL make/models will havevariations in the anterior or posterior curvatures or in its thickness,which will affect the values of the constants in equations (1a) and(1b). Depending on the magnitude of the differences with the IOL used inthis example, it is anticipated that the S₂, S₃, S₄ and the W₂ W₃ W₄constants (for the respective equations (1a) and (1b)) will vary by upto approximately 5% (per constant), which in turn will affect thecalculation of S₁ and W₁ by up to approximately 10% (cumulative). Itshould be noted that the constants in equations (1a) and (1b) may alsovary and be affected depending on many other factors, non-limiting,non-exhaustive listing of examples of which may include the type of IOLused (as mentioned), the type and the manner in which an ophthalmicsurgery is performed, the experience of the physician performing thesurgery, whether the phacoemulsification was uneventful or hadcomplications, and etc.

The accuracy of the new formula's (equations 1a and 1b) IOL powercalculations is evaluated by comparing them with the four most commonlyused intraocular lens power formulas, which are the SRK/T, Holladay 1,Hoffer Q and the Haigis. These formulas are programmed within mostbiometry/keratometry units and on different computer programs. All fourformulas are based on geometric optics and use thin lens vergenceequations in which each lens is reduced to a power at its principleplane. The position of each principle plane depends on the lens powerand its anterior and posterior curvatures. Although all four formulasuse the same optical principles, they differ from each other in the waythey estimate the position of the surgically implanted IOL, a valueoften referred to as the Estimated Lens Position (ELP).

Each of these formulas uses a different algorithm based on certainpre-operative measurements. The SRK/T, Holladay 1 and the Hoffer Q basetheir algorithm on the axial length of the eye and the radius ofcurvature of the anterior corneal surface. These ELP values do notrepresent the true position of the IOL. Instead, these algorithms wereobtained by analyzing clinical data and adjusting the calculatedresultant refractive error in these cases to match the actualpost-operative refractive result. The calculated ELP values are labeledthe formulas' constants, i.e. the “A” constant for the SRK/T formula,the “SF” constant for the Holladay 1 formula and the “pACD” constant forthe Hoffer Q formula. Although most manufacturers give a specific “A”constant to each IOL model, surgeons are advised to “personalize” theconstants by reviewing a minimum of 20 cases and adjusting the constantsuntil the mean difference between the calculated resultant refractiveerror and the actual post-operative refractive result becomes zero.

Using the thick lens algorithm for IOL power calculation, Haigis1calculated an IOL position estimate by means of multiple regressionanalysis performed on preoperative data. The highest correlationcoefficient (0.68) was with the anterior chamber depth, a result thatclosely parallels ours (0.66). In his formula, Haigis estimates thepostoperative ACD as a function of the preoperative ACD and the AL.

Table 3 is an evaluation of the EAPD in accordance with the presentinvention (row 1) and used within the IOL power formula (Equations 1aand or 1b) compared with other commonly used formulas.

TABLE 3 Prediction errors with the present formula compared to theerrors obtained with the Haigis, Hoffer Q, Holladay 1, and SKR/Tformulas Prediction errors (% of patients) Within Within Over FormulaMed AE Range +/−0.50 D +/−1.00 D 1.00 D Present Invention 0.30 −1.01 to0.98 71 (78.9%) 89 (98.9%) 1 (1.1%) (Eq 1a and or 1b) Haigis 0.37 −1.40to 1.30 64 (71.1%) 86 (95.5%) 4 (4.4%) Hoffer Q 0.35 −1.11 to 1.11 57(63.3%) 88 (97.8%) 2 (2.2%) Holladay 1 0.36 −1.10 to 1.08 62 (68.9%) 88(97.8%) 2 (2.2%) SRK/T 0.35 −1.12 to 1.01 62 (68.9%) 88 (97.8%) 3 (3.3%)

Table 3 shows the prediction errors with the present formula (equations1a and or 1b) compared to the errors obtained with the Haigis, Hoffer Q,Holladay and SRK/T formulas. The accuracy of the new formula's IOL powercalculations (equations 1a or 1b) is evaluated by comparing its medianabsolute error (MedAE) to the ones obtained with the other formulas. Themedian values are reported for the absolute prediction errors instead ofthe mean values because these absolute values do not fit a Gaussiancurve distribution. The MedAE was noted to be lower with the presentformula compared to the other formulas. Also, the percentage of patientswith an accuracy of within +/−0.50 D+/−1.00 D was higher with thepresent formula (equations 1a or 1b) compared to the other formulas.

Although the invention has been described in considerable detail inlanguage specific to structural features and or method acts, it is to beunderstood that the invention defined in the appended claims is notnecessarily limited to the specific features or acts described. Rather,the specific features and acts are disclosed as exemplary preferredforms of implementing the claimed invention. Stated otherwise, it is tobe understood that the phraseology and terminology employed herein, aswell as the abstract, are for the purpose of description and should notbe regarded as limiting. Therefore, while exemplary illustrativeembodiments of the invention have been described, numerous variationsand alternative embodiments will occur to those skilled in the art. Forexample, the new measurements used to establish the Equations 1a and 1bwere made by optical biometry using the LENSTAR LS-900 biometer fromHAAG-STREIT, INC. More specifically, these newly described measurementsinclude the anterior cortical distance (ACX), nucleus thickness (NT),posterior cortical distance (PCX), ante nucleus distance (AND) and theretro nucleus distance (RND). Such measurements can also be made withother optical biometers, ultrasound units, optical coherence tomography(OCT) units and other one-dimensional, two-dimensional orthree-dimensional imaging units. Further, the intraocular lens powercalculation formula uses thin lens optics. Such calculations can alsouse thick lens optics, ray-tracing and different other computerizedprograms to calculate the IOL power. Such variations and alternateembodiments are contemplated, and can be made without departing from thespirit and scope of the invention.

It should further be noted that throughout the entire disclosure, thelabels such as left, right, front, back, top, bottom, forward, reverse,clockwise, counter clockwise, up, down, or other similar terms such asupper, lower, aft, fore, vertical, horizontal, oblique, proximal,distal, parallel, perpendicular, transverse, longitudinal, etc. havebeen used for convenience purposes only and are not intended to implyany particular fixed direction or orientation. Instead, they are used toreflect relative locations and/or directions/orientations betweenvarious portions of an object.

In addition, reference to “first,” “second,” “third,” and etc. membersthroughout the disclosure (and in particular, claims) is not used toshow a serial or numerical limitation but instead is used to distinguishor identify the various members of the group.

In addition, any element in a claim that does not explicitly state“means for” performing a specified function, or “step for” performing aspecific function, is not to be interpreted as a “means” or “step”clause as specified in 35 U.S.C. Section 112, Paragraph 6. Inparticular, the use of “step of,” “act of” “operation of,” or“operational act of” in the claims herein is not intended to invoke theprovisions of 35 U.S.C. 112, Paragraph 6.

What is claimed is:
 1. A method for determine preoperative estimation ofpostoperative IOL position, comprising: determining an axial length (AL)of an eye; determining Ante-Nucleus Distance (AND), which is a distancefrom an anterior surface of cornea along an optical axis of the eye toan anterior surface of a natural lens nucleus; determining Retro-NucleusDistance (RND), which is a distance from an anterior surface of thenatural lens nucleus to a posterior surface of a natural lens capsule;with an Estimated Anterior Pseudophakic Distance (EAPD) calculatedaccording:EAPD=W ₁+(W ₂×AND)+(W ₃×RND)+(W ₄×AL), Where W₁, W₂, W₃, and W₄ areconstant coefficients.
 2. The method for determine preoperativeestimation of postoperative IOL position, as set forth in claim 1,where: AND is determined as follows:AND=ACD+ACX; where: ACD is the Anterior Chamber Depth defined by adistance from an anterior surface of cornea along an optical axis of theeye to an anterior surface of a natural lens, which is an anteriorsurface of the lens capsule; and ACX is the Anterior Cortical Spacedefined by a distance from the anterior surface of the natural lens,which is the anterior surface of the lens capsule, along an optical axisof the eye to the anterior surface of the lens nucleus.
 3. The methodfor determine preoperative estimation of postoperative IOL position, asset forth in claim 1, where: RND is determined as follows:RND=NT+PCX; where: NT is defined by a distance measured along an opticalaxis from an anterior lens nucleus surface to a posterior lens nucleussurface of the natural lens; PCX is the Posterior Cortical Space definedby a distance from the posterior surface of the natural lens nucleusalong an optical axis of the eye to the posterior surface of the lens,which is the posterior surface of the lens capsule.
 4. The method fordetermine preoperative estimation of postoperative IOL position, as setforth in claim 1, further comprising: determining a refractive power ofa cornea of the eye; and measuring Anterior Chamber Depth, which is adistance that spans from anterior corneal surface to an anterior naturallens surface.
 5. The method for determine preoperative estimation ofpostoperative IOL position as set forth in claim 1, where: the axiallength of the eye is a distance from an anterior surface of cornea alongan optical axis of the eye to an anterior surface of the retina within afovea region of the eye.
 6. The method for determine preoperativeestimation of postoperative IOL position as set forth in claim 2, where:the optical axis is a reference line along which light propagatesthrough the eye.
 7. The method for determine preoperative estimation ofpostoperative IOL position as set forth in claim 1, where: therefractive power of cornea is determined by: measuring a radius ofcurvature of the cornea (CR); and converting the cornea radius into acorneal refractive power K using index of refraction.
 8. The method fordetermine preoperative estimation of postoperative IOL position, as setforth in claim 1, wherein: Intraocular estimated power IOL_(EP) isdetermined by:${IOL}_{EP} = {\frac{n_{AH}}{{AL} - {EAPD}} - \frac{1}{\frac{1}{K + R_{C}} - \frac{EAPD}{n_{AH}}}}$where: n_(AH) is the index of refraction for the aqueous humor; K iscorneal power; and R_(C) is refractive error at the corneal plane. 9.The method for determine preoperative estimation of postoperative IOLposition, as set forth in claim 1, wherein: constant coefficients W₁,W₂, W₃, and W₄ are statically derived using linear regression.
 10. Themethod for determine preoperative estimation of postoperative IOLposition, as set forth in claim 1, wherein: constant coefficients W₁,W₂, W₃, and W₄ are statically derived using linear, single, andsequential regressions.
 11. A method for determine preoperativeestimation of postoperative IOL position, comprising: determining anaxial length (AL) of an eye; determining Ante-Nucleus Distance (AND),which is a distance from an anterior surface of cornea along an opticalaxis of the eye to an anterior surface of a natural lens nucleus;determining natural lens Nucleus Thickness (NT), which is a distancemeasured along an optical axis from an anterior surface of a lensnucleus to a posterior surface of the lens nucleus; with an EstimatedAnterior Pseudophakic Distance (EAPD) calculated according:EAPD=S ₁+(S ₂×AND)+(S ₃×NT)+(S ₄×AL), Where S₁, S₂, S₃, and S₄ areconstant coefficients.
 12. The method for determine preoperativeestimation of postoperative IOL position, as set forth in claim 11,where: AND is determined as follows:AND=ACD+ACX; where: ACD is the Anterior Chamber Depth defined by adistance from an anterior surface of cornea along an optical axis of theeye to an anterior surface of a natural lens, which is an anteriorsurface of the lens capsule; and ACX is the Anterior Cortical Spacedefined by a distance from the anterior surface of the natural lens,which is the anterior surface of the lens capsule, along an optical axisof the eye to the anterior surface of the lens nucleus.
 13. The methodfor determine preoperative estimation of postoperative IOL position, asset forth in claim 11, further comprising: determining a refractivepower of a cornea of the eye; and measuring Anterior Chamber Depth,which is a distance that spans from anterior corneal surface to ananterior natural lens surface.
 14. The method for determine preoperativeestimation of postoperative IOL position as set forth in claim 11,where: the axial length of the eye is a distance from an anteriorsurface of cornea along an optical axis of the eye to an anteriorsurface of the retina within a fovea region of the eye.
 15. The methodfor determine preoperative estimation of postoperative IOL position asset forth in claim 11, where: the optical axis is a reference line alongwhich light propagates through the eye.
 16. The method for determinepreoperative estimation of postoperative IOL position as set forth inclaim 11, where: the refractive power of cornea is determined by:measuring a radius of curvature of the cornea (CR); and converting thecornea radius into a corneal refractive power K using index ofrefraction.
 17. The method for determine preoperative estimation ofpostoperative IOL position, as set forth in claim 10, whereinintraocular estimated power IOL_(EP) is determined by:${IOL}_{EP} = {\frac{n_{AH}}{{AL} - {EAPD}} - \frac{1}{\frac{1}{K + R_{C}} - \frac{EAPD}{n_{AH}}}}$where: n_(AH) is the index of refraction for the aqueous humor; K iscorneal power; and R_(C) is refractive error at the corneal plane. 18.The method for determine preoperative estimation of postoperative IOLposition, as set forth in claim 11, wherein: constant coefficients S₁,S₂, S₃, and S₄ are statically derived using linear regression.
 19. Themethod for determine preoperative estimation of postoperative IOLposition, as set forth in claim 11, wherein: constant coefficients S₁,S₂, S₃, and S₄ are statically derived using linear, single, andsequential regressions.
 20. The method for determine preoperativeestimation of postoperative IOL position, as set forth in claim 11,where: NT is determined as follows:NT=LT−PCX−ACX where: LT is a distance measured along an optical axisfrom an anterior lends capsule surface to the posterior lends capsulesurface of lens; PCX is the Posterior Cortical Space defined by adistance from the posterior surface of the natural lens nucleus along anoptical axis of the eye to the posterior surface of the lens, which isthe posterior surface of the lens capsule; and ACX is the AnteriorCortical Space defined by a distance from the anterior surface of thenatural lens nucleus along an optical axis of the eye to the anteriorsurface of the lens, which is the anterior surface of the lens capsule.